Straight Line Motion with a Stomper

Ann Brandon                    Joliet West High School
                               401 North Larkin Ave
                               Joliet IL 60435
                               (815) 727-6950

Objectives:

After this experience, the student should
   1.  be able to define average speed (distance traveled/time)
   2.  be able to graph distance vs time and velocity vs time
   3.  be able to find the velocity from the distance time graph (slope)
   4.  be able to find the acceleration from the velocity time graph (slope)
   5.  recognize constant velocity, constant acceleration and changing 
       acceleration from the shape of the distance-time and velocity-time graphs

Materials needed:

   (for each group)
Stopwatch, meter stick, Stomper (battery powered toy car), large washer or 100 g
mass, tape, paper tape (ticker tape) and a recording (ticker tape) timer, 
Tricycle (optional).

Strategy:

     Part I:  Begin with the Stomper.  Show it going in a straight line along 
the counter top.  Ask:  How fast is it going?  What do we need to know to find 
out?  (You need a distance traveled and a time.)  Give each group a Stomper, 
stopwatch and meter stick.  They should determine the average speed of their 
Stomper.  It should take 10 or 15 minutes for them to do several trials. 

     Part II:  How fast was the Stomper going as it moved along?  Was it going 
the same speed everywhere or did it speed up or slow down?  Point out:  The 
stopwatch is only good for substantial times, several seconds.  It will not help 
us answer this question.  Demonstrate the recording timer by pulling a meter or 
so of tape through it.  Explain why the time intervals are equal and ask why the 
spaces are not even.  (The spaces are small where the speed was small.) 

     Each group should do two runs with the Stomper pulling a length of ticker 
tape behind it.  Mark off each tape in groups of six dots.  (Each six is one 
tenth of a second.)  The first tape will become a distance-time graph.  Rip each 
six dot section and glue it to a piece of graph paper.  The first section goes 
on next to the origin.  The second section goes over one width of tape, but 
starts up, so that its bottom is next to the first tapes' top.  The third goes 
over one and its bottom lines up with the top of the second section, etc.  Thus 
the vertical axis is the distance traveled in cm. and the horizontal axis is 
the time in tenths of a second.  This graph will have a constant slope equal to 
the average speed found with the stopwatch.  Demonstrate how to find slope. 

     The second tape will become a velocity-time graph.  Each six dot section is 
the distance traveled per tenth of a second, so it is the average velocity for 
that tenth of a second.  For this graph the vertical axis is the velocity in cm 
per tenth of a second, while the horizontal axis is again the time in tenths of 
a second.  For this graph, each tape has its bottom on the horizontal axis.  The 
tapes go next to each other in order.  This graph will have a slope very close 
to zero because the speed is very close to being constant.  How did this 
velocity compare to the slope of the first graph?  How did it compare to the 
speed found with the stopwatch? 

     Be certain that you ask the students to describe each of these two graphs 
and to compare them to each other. 

     This is probably as much as you can expect for one day.  I would then spend 
a day or so doing constant velocity problems to reinforce this concept. 

     Part III:  Constant Acceleration
     Drop a mass.  (Catch it!)  Ask if this is constant velocity.  Ask how you 
can find out.  Using the recording timers, attach the tape to the mass and drop 
the mass over the side of the table.  (It pays to protect the floor with a book, 
or a newspaper.)  Run two tapes.  Mark every sixth dot and create a distance-
time and a velocity-time graph.  Look at them!  The distance graph will not be a 
straight line this time.  It should look like a parabola, because the speed is 
increasing, the slope will increase.  The velocity graph will be a straight 
line, but will not be horizontal, because the speed is increasing at a constant 
rate. The slope of this line is the acceleration.  (The change in velocity/the 
time it took (dV/dt).) 

     Again, it is very important to ask what these graphs look like and to 
compare them to each other and to the graphs from Part II. 

     This is probably a second day's work.  It should be followed by problems 
with distance, velocity and constant acceleration. 

     Part IV:  Constantly Increasing Acceleration
     Lay a chain on the counter top.  Push it over the edge one link at a time, 
until it goes by itself.  Ask what kind of motion this is.  Again, we can 
analyze this motion if we attach a tape to it.  Mark every sixth dot.  The 
distance time graph is optional, be sure to do a velocity time graph.  This will 
not be a straight line because the velocity increases at an increasing rate.
(The acceleration (slope) increases at a constant rate, thus we get a parabola.) 

     It is once more imperative that you ask the students to describe the shape 
of the graph(s) and compare them to the previous graphs. 

Optional:  Have Tricycle races.  Have someone ride a tricycle pulling ticker 
tape.  The velocity-time graph is the most interesting.  Be sure to ask about 
the accelerations.  They will be positive and negative!

Conclusions:

  Velocity is the distance traveled/time it took (dD/dt)
  Velocity is the slope of a distance-time graph
  Acceleration is the change in velocity/time it took (dV/dt)
  Acceleration is the slope of a velocity-time graph
  Constant velocity gives straight line graphs for both d-t and v-t
  Constant acceleration gives parabolas for d-t, but straight lines for v-t
  Changing acceleration gives v-t graphs with changing slopes 

Performance Assessment:

    Using TWO SPEED Racer (a friction car, about $2.75 at "Toys R Us"): Show it 
to the students.  Placing it on a flat surface, where all of them can watch it, 
pull it back until you hear a click.  Let it go.  It will go in a straight line, 
and suddenly increase its speed.
    Ask the students to sketch two graphs.  A Distance vs Time and a Velocity vs 
Time graph.

Rubric:

5 pts  Graphs are correctly labeled on each axis. Distance-time graph shows as 
       short straight line, sloping up followed by a steeper straight line; also 
       sloping up.
       Velocity-time graph shows a short, horizontal line, followed by a higher 
       horizontal line.
4 pts  Graphs not correctly labeled, but show the proper shapes.
3 pts  Graphs not correctly labeled, and only one of the graphs shows the proper 
       shape.
2 pts  Graphs properly labeled, but neither graph is the proper shape.
0 pt   No labels, and wrong shapes.

Multicultural Applications:

    There are many applications of distance vs time in life including the Summer 
Olympics track competitions and the speed skating and cross country skiing in 
the Winter Olympics.